Method for determining permeability at high pressure based on low pressure porosity and permeability of tight sandstone and application thereof

Abstract

The application discloses a method for determining the permeability under high pressure based on the low-pressure porosity and permeability of compact sandstone and application thereof. The porosity and permeability under low pressure are obtained through core analysis, and then the T2 spectrum data under the same low pressure are measured by using nuclear magnetic resonance, and the T2 geometric mean value is calculated to determine the SDR model parameters. Then, a relationship diagram of the T2 geometric mean value and the corresponding pressure is established, the T2 geometric mean value under high pressure is obtained through nonlinear regression, and then the permeability of the core under different high pressures is calculated. The method only needs the porosity and permeability values under several low pressures and the T2 geometric mean value under the corresponding pressure, overcomes the problem of complicated parameter determination of the traditional nuclear magnetic resonance permeability model, and can determine the parameters of a core, and also overcomes the problems of difficulty in pressurization of some instruments, incapability of measuring the core permeability under high pressure and long test time.

Description

Technical Field

[0001] This invention relates to a method for determining permeability under high pressure, and more particularly to a method for determining permeability under high pressure based on low-pressure porosity and permeability of dense sandstone and its application. Background Technology

[0002] Permeability is a measure of oil and gas flow capacity and a key parameter in reservoir evaluation. Currently, deep and ultra-deep oil and gas exploration and development has become a major objective in my country. However, the great depth of these reservoirs leads to extremely high overlying formation pressures. For example, the deep tight oil and gas reservoirs of the Cretaceous Qingshuihe Formation in the southern margin of the Junggar Basin have overlying formation pressures reaching 150 MPa, classifying them as ultra-high-pressure reservoirs. Such high pressures inevitably have a significant impact on reservoir properties, and how to assess reservoir permeability under high pressure has always been a key research focus.

[0003] Currently, reservoir permeability is primarily assessed through laboratory core permeability measurements. Methods include steady-state methods, instantaneous pressure pulse methods, and nuclear magnetic resonance (NMR) methods. Permeability is measured under different effective pressures by applying confining pressure or pore pressure. The steady-state method involves injecting gas at a certain pressure into one end of the rock sample, maintaining a stable flow rate at the other end per unit time, and then calculating permeability using Darcy's law. The pulse method involves saturating the rock sample with gas at a certain pressure, then reducing the downstream pressure to create a pulse pressure difference between the upstream and downstream ends, establishing a functional relationship between the upstream and downstream pressure difference and time to calculate permeability. Conventional NMR techniques mainly measure permeability using SDR and Timur / Coates models. T2 spectra can also be used to analyze pore size distribution. The SDR model simply averages the pore size distribution and uses the geometric mean of the T2 distribution to estimate permeability; the Timur / Coates model uses porosity, bound water saturation, and free fluid index to predict permeability.

[0004] While the steady-state method is one of the most common testing methods, its lower limit of measurement is approximately 0.1 mD, and it requires a long time for the flow rate to stabilize, especially for low-permeability rock samples, where permeability measurement becomes even more difficult after pressurization. The instantaneous pressure pulse method is similar, typically requiring the pressure difference to reach one-third of the initial pressure difference before measurement stops, which is still time-consuming under high pressure. Furthermore, most instruments struggle to apply confining or pore pressure to the core, making it difficult to reach the overlying formation pressures in deep and ultra-deep layers. Under high pressure, instruments also suffer from short lifespans and poor reliability. Conventional nuclear magnetic resonance (NMR) predicts permeability through models, but determining the parameters in the model generally requires repeated experiments with multiple cores, making parameter determination complex. Cores are inherently heterogeneous, making parameter accuracy difficult to guarantee. Moreover, this model is typically used to measure porosity and permeability under normal or low pressure, with limited application in high-pressure porosity and permeability testing.

[0005] The apparatus described in patent CN114062215B, which describes a high-pressure permeability measurement experimental device and evaluation method for rock cores, suffers from the aforementioned defects: the equipment setup is complex, the cost is high, and the time required is long. Summary of the Invention

[0006] The purpose of this invention is to overcome the problems of traditional permeability testing methods being time-consuming, difficult to apply high pressure to some instruments, and difficult to determine the parameters of nuclear magnetic resonance permeability models. It provides a method for determining nuclear magnetic resonance permeability model parameters based on the low-pressure porosity and permeability results of dense sandstone, and for determining permeability under high pressure.

[0007] A method for determining permeability under high pressure based on low-pressure porosity and permeability of tight sandstone includes the following steps:

[0008] Step (1): Measure the porosity and permeability at at least three points under low pressure using a conventional porosimeter as initial values;

[0009] Step (2): Take the three pressure points in step (1) as the pressure points of the nuclear magnetic resonance experiment, obtain the T2 spectrum data at the same pressure point, and calculate the average T2 value;

[0010] Step (3): Determine the relevant empirical parameters C, m, and n of the SDR model by combining the porosity and permeability measured in step (1) with the corresponding T2 geometric mean obtained in step (2);

[0011] Step (4): Establish the relationship between the corresponding geometric mean T2 obtained in step (2) and the corresponding pressure;

[0012] Step (5): Obtain the geometric mean of T2 under high pressure through nonlinear regression of the relationship graph;

[0013] Step (6): Predict porosity under high pressure based on the change of the geometric mean of T2 and the initial porosity;

[0014] Step (7): Substitute the T2 geometric mean from step (5) and the porosity from step (6) into the model established in step (3) to calculate the permeability under this pressure.

[0015] Furthermore, the permeability test data of the core analysis mentioned in step (1) is obtained in accordance with the procedure in the standard "Core Analysis Methods SY / T5336-2006".

[0016] Furthermore, the nuclear magnetic resonance T2 spectrum experimental data of the core analysis described in steps (2) and (3) were obtained in accordance with the procedures specified in the standard "Laboratory Measurement Specification for Nuclear Magnetic Resonance Parameters of Rock Samples SY / T6490-2007".

[0017] The formula for calculating the geometric mean of T2 in nuclear magnetic resonance imaging is as follows:

[0018]

[0019] In the formula, T 2gm The geometric mean of the T2 NMR spectrum is given in milliseconds (ms); φ i For the corresponding component T 2i Porosity component, in %; φ nmr NMR porosity, expressed as a percentage.

[0020] The formula for calculating NMR porosity is as follows:

[0021]

[0022] In the formula, S is the T2 spectral amplitude, in %; T2 is the transverse relaxation time measured by NMR, in ms; T 2min The initial value of the T2 spectrum relaxation time is given in milliseconds (ms). 2max This represents the termination value of the T2 spectrum relaxation time, in milliseconds (ms).

[0023] Furthermore, the SDR penetration model in step (3) is as follows:

[0024]

[0025] In the formula, φ represents porosity, in %; k NMR Permeability, in mD; T 2g T2 represents the geometric mean, in milliseconds (ms); C, m, and n are model constants.

[0026] Furthermore, the porosity prediction formula in step (6) is as follows:

[0027]

[0028] In the formula, φ represents porosity, expressed as a percentage (%). o Initial porosity, in %; The initial T2 geometric mean is expressed in milliseconds (ms). T2 is the geometric mean value under the current pressure, in milliseconds (ms).

[0029] Compared with the prior art, the beneficial effects of the technical solution of the present invention are as follows:

[0030] This invention obtains porosity and permeability under low pressure through core analysis, and then determines the SDR model parameters by combining T2 spectrum data obtained from nuclear magnetic resonance (NMR) at the same low pressure and calculating the T2 geometric mean. A relationship graph between the T2 geometric mean and the corresponding pressure is then established, and the T2 geometric mean under high pressure is obtained through nonlinear regression. Finally, the permeability of the core under different high pressures is calculated. This method requires only a few porosity and permeability values ​​at low pressures, as well as the corresponding T2 geometric mean under the pressure, overcoming the cumbersome parameter determination problem of traditional NMR permeability models. It can determine the parameters using only one core sample, and also overcomes the problems of some instruments being difficult to pressurize, unable to measure core permeability under high pressure, and having long testing times. Attached Figure Description

[0031] Figure 1 The T2 nuclear magnetic resonance spectra of SD-1 tight sandstone under different pressures as described in the embodiments of the present invention;

[0032] Figure 2 The T2 nuclear magnetic resonance spectra of SD-2 tight sandstone under different pressures as described in the embodiments of the present invention;

[0033] Figure 3 This is a graph showing the relationship between the geometric mean value of T2 and pressure in the No. 1 tight sandstone according to an embodiment of the present invention;

[0034] Figure 4 This is a graph showing the relationship between the geometric mean value of T2 and pressure in the No. 2 tight sandstone according to an embodiment of the present invention.

[0035] Figure 5 This is a comparison chart of the calculated permeability and core analysis permeability of two dense sandstone blocks described in an embodiment of the present invention. Detailed Implementation

[0036] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to embodiments. The content mentioned in the embodiments is not intended to limit the present invention.

[0037] This invention provides a method for determining permeability under high pressure based on low-pressure porosity and permeability of dense sandstone, comprising the following steps:

[0038] Step (1): Perform routine physical property tests on shale cores. The core porosity and permeability analysis were conducted according to the procedures specified in the standard "Core Analysis Methods SY / T5336-2006" to obtain porosity and permeability under confining pressures of 0.5, 2, 5, 7, 10, 15, 20, and 30 MPa. The porosity and permeability at 0.5, 2, 5, and 7 MPa were used as initial low-pressure values ​​to determine model parameters, and the remaining values ​​were compared with the calculated permeability.

[0039] Step (2): Nuclear magnetic resonance (NMR) T2 spectroscopy experiments were performed on water-saturated tight sandstone cores to obtain NMR T2 spectral data at 0.5, 2, 5, 7, 10, and 15 MPa. The core NMR T2 experiments were conducted according to the procedures specified in the standard "Laboratory Measurement Specification for Nuclear Magnetic Resonance Parameters of Rock Samples SY / T6490-2007". The average T2 values ​​at 0.5, 2, 5, and 7 MPa were calculated to determine the model parameters.

[0040] The formula for calculating the geometric mean of T2 in nuclear magnetic resonance imaging is as follows:

[0041]

[0042] In the formula, T 2gm The geometric mean of the T2 NMR spectrum is given in milliseconds (ms); φ i For the corresponding component T 2i Porosity component, in %; φ nmr NMR porosity, expressed as a percentage.

[0043] The formula for calculating NMR porosity is as follows:

[0044]

[0045] In the formula, S is the T2 spectral amplitude, in %; T2 is the transverse relaxation time measured by NMR, in ms; T 2min The initial value of the T2 spectrum relaxation time is given in milliseconds (ms). 2max This represents the termination value of the T2 spectrum relaxation time, in milliseconds (ms).

[0046] Step (3): Determine the relevant empirical parameters C, m, and n of the SDR model by combining the porosity and permeability measured in step (1) with the corresponding T2 geometric mean obtained in step (2). Finally, the C of SD-1 tight sandstone is 192, m is 3.1, and n is 1.5, and the C of SD-2 tight sandstone is 200, m is 3.1, and n is 1.3.

[0047] Step (4): Establish the relationship between the corresponding geometric mean T2 obtained in step (2) and the corresponding pressure, see Figure 1-2 The geometric mean of T2 has a good relationship with pressure.

[0048] Step (5): The geometric mean of T2 at 10, 15, 20, and 30 MPa is obtained by nonlinear regression of the relationship graph. The values ​​of SD-1 and SD-2 are 4.2755, 4.1079, 3.9468, 3.6434 and 4.1366, 4.0143, 3.8957, 3.6688, respectively.

[0049] Step (6): Using the T2 geometric mean obtained from the regression in step (5) and the initial porosity and the initial T2 geometric mean, the porosity of SD-1 and SD-2 at 10, 15, 20, and 30 MPa is calculated to be 14.64%, 14.06%, 13.51%, 12.47% and 12.41%, 12.04%, 11.69%, 11.01%, respectively.

[0050] Step (7): Substitute the regression T2 geometric mean and the calculated porosity into the model established in step (3) to calculate the permeability under this pressure. The calculation results are compared with those of... Figure 3 .

[0051] The results of conventional physical property experiments and nuclear magnetic resonance T2 spectroscopy analysis of the core are shown in Table 1.

[0052] Table 1

[0053]

[0054]

[0055] Note: * indicates the geometric mean of T2.

[0056] Experimental conclusion: From Figure 1-5 As can be seen from Table 1, the permeability determination method of this embodiment is basically consistent with the measured results of other testing methods. This embodiment overcomes the problem of the cumbersome parameter determination of the traditional nuclear magnetic resonance permeability model and can determine its parameters through a rock core. It also overcomes the problems of some instruments being difficult to pressurize, unable to measure the permeability of the rock core under high pressure, and having a long testing time.

[0057] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless specifically defined as herein.

[0058] It should be understood that the above detailed description of the technical solutions of the present invention with reference to preferred embodiments is illustrative and not restrictive. Those skilled in the art can modify the technical solutions described in the embodiments or make equivalent substitutions for some of the technical features based on reading this specification; however, these modifications or substitutions do not cause the essence of the corresponding technical solutions to depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for determining permeability under high pressure based on low-pressure porosity and permeability of tight sandstone, characterized in that: Includes the following steps: Step (1): Measure the porosity and permeability at at least three points under low pressure as initial values; Step (2): Take the three points in step (1) as the pressure points of the nuclear magnetic resonance experiment, obtain the nuclear magnetic resonance T2 spectrum data at the same pressure point, and calculate the geometric mean of T2. Step (3): Determine the empirical parameters C, m, and n of the SDR model by combining the porosity and permeability measured in step (1) with the corresponding T2 geometric mean obtained in step (2); Step (4): Establish the relationship between the corresponding geometric mean of T2 obtained in step (2) and the corresponding pressure; Step (5): Obtain the geometric mean of T2 under high pressure through nonlinear regression of the relationship graph; Step (6): Predict porosity under high pressure based on the change of the geometric mean of T2 and the initial porosity; Step (7): Substitute the T2 geometric mean from step (5) and the porosity from step (6) into the model established in step (3) to calculate the permeability under this pressure; The SDR penetration model in step (3) is as follows: (3) In the formula, Porosity, expressed as % Permeability, in mD; T 2g The geometric mean of T2 is expressed in milliseconds (ms); C, m, and n are model constants. The porosity prediction formula in step (6) is as follows: (4) ； In the formula, Porosity, expressed as % Initial porosity, in percentages (%) The initial T2 geometric mean is expressed in milliseconds (ms). T2 is the geometric mean value under the current pressure, in milliseconds (ms).

2. The method according to claim 1, characterized in that: The formula for calculating the geometric mean of T2 in nuclear magnetic resonance imaging is as follows: In the formula, T 2gm The value is the geometric mean of the nuclear magnetic resonance T2 spectrum, expressed in milliseconds (ms). For the corresponding component T 2i Porosity component, in % %. NMR porosity, in % The formula for calculating NMR porosity is as follows: ； In the formula, S is the T2 spectral amplitude, in %; T2 is the transverse relaxation time measured by NMR, in ms; T 2min The initial value of the T2 spectrum relaxation time is given in milliseconds (ms). 2max This represents the termination value of the T2 spectrum relaxation time, in milliseconds (ms).

3. The method for determining permeability under high pressure based on low-pressure porosity and permeability of tight sandstone according to any one of claims 1-2 is used in determining core permeability and / or reservoir permeability.

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